User Andrea

116 votes

Finite subgroups of the multiplicative group of a field are cyclic

abstract-algebra group-theory

answered Aug 26, 2011 at 14:33

42 votes

Similar matrices and field extensions

answered Aug 13, 2011 at 17:06

35 votes

If the localization of a ring $R$ at every prime ideal is an integral domain, must $R$ be an integral domain?

abstract-algebra commutative-algebra ring-theory ideals

answered May 19, 2012 at 11:09

17 votes

Accepted

Motivation behind the definition of flat module

commutative-algebra modules motivation flatness

answered Apr 21, 2012 at 23:56

17 votes

Accepted

Is the number of prime ideals of a zero-dimensional ring stable under base change?

algebraic-geometry ring-theory ideals

answered Aug 13, 2011 at 19:12

15 votes

The total ring of fractions of a reduced Noetherian ring is a direct product of fields

abstract-algebra ring-theory commutative-algebra noetherian

answered Aug 8, 2011 at 17:42

15 votes

Primary ideals of Noetherian rings which are not irreducible

commutative-algebra ideals noetherian

answered Aug 18, 2011 at 22:26

15 votes

Accepted

Is the radical of an irreducible ideal irreducible?

commutative-algebra

answered Feb 6, 2012 at 11:38

10 votes

Accepted

In $K[X,Y]$, is the power of any prime also primary?

commutative-algebra ideals

answered Feb 24, 2012 at 19:36

10 votes

A square matrix has the same minimal polynomial over its base field as it has over an extension field

linear-algebra

answered Sep 23, 2011 at 10:05

9 votes

Are there Zariski-continuous maps between algebraic sets that are not polynomial maps?

algebraic-geometry zariski-topology

answered Aug 18, 2011 at 19:09

9 votes

Accepted

Linearly disjoint field extensions

field-theory

answered Aug 14, 2011 at 14:58

9 votes

Accepted

Intersection of irreducible components of a smooth curve

algebraic-geometry

answered May 18, 2012 at 19:38

8 votes

When do two matrices have the same column space?

linear-algebra matrices numerical-linear-algebra

answered Mar 24, 2013 at 23:25

8 votes

Noetherian integral domain such that $m/m^2$ is a one-dimensional vector space over $A/m$

abstract-algebra commutative-algebra ring-theory

answered Aug 18, 2011 at 19:38

8 votes

What is the differences between scheme-theoretical intersection and set-theoretical intersection?

algebraic-geometry representation-theory

answered Aug 30, 2011 at 18:43

8 votes

Proving $2,3,1+\sqrt{-5}$ and $1-\sqrt{-5}$ are irreducible in $\mathbb{Z}[\sqrt{-5}]$

abstract-algebra ring-theory

answered Nov 28, 2011 at 14:33

8 votes

Accepted

Knot with genus $1$ and trivial Alexander polynomial?

algebraic-topology differential-geometry differential-topology knot-theory

answered Jan 4, 2012 at 21:06

7 votes

Accepted

Artinian local $k$-algebra

commutative-algebra

answered Dec 30, 2011 at 15:28

7 votes

Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?

linear-algebra matrices

answered Apr 25, 2012 at 15:28

6 votes

Invertible modules are locally free of rank 1

commutative-algebra

answered Dec 27, 2011 at 12:23

6 votes

Prove that an infinite ring with finite quotient rings is an integral domain

abstract-algebra ring-theory integral-domain

answered Mar 30, 2012 at 10:04

6 votes

Spectrum of finite $k$-algebras

commutative-algebra

answered May 15, 2012 at 15:41

6 votes

Accepted

Is there a $C^\infty$ function $f$ s. t. the convergent radius of Maclaurin series of $f$ is $0$?

calculus power-series

answered May 20, 2012 at 7:44

6 votes

Accepted

Homology of $\mathbb{R}^3 - S^1$

algebraic-topology

answered Aug 14, 2011 at 10:03

6 votes

Similar matrices and field extensions

linear-algebra abstract-algebra matrices extension-field

answered Aug 23, 2011 at 12:14

6 votes

How to Compute Genus

algebraic-geometry arithmetic-geometry

answered Aug 8, 2011 at 8:50

5 votes

Accepted

Stalk of coherent sheaf vanishing

algebraic-geometry

answered Aug 13, 2011 at 14:17

5 votes

Accepted

Is invertibility a stalk-local property?

algebraic-geometry schemes

answered Nov 19, 2011 at 12:02

5 votes

How to calculate the determinant of all-ones matrix minus the identity?

linear-algebra matrices determinant

answered Nov 21, 2011 at 13:26

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73 Answers

Finite subgroups of the multiplicative group of a field are cyclic

Similar matrices and field extensions

If the localization of a ring $R$ at every prime ideal is an integral domain, must $R$ be an integral domain?

Motivation behind the definition of flat module

Is the number of prime ideals of a zero-dimensional ring stable under base change?

The total ring of fractions of a reduced Noetherian ring is a direct product of fields

Primary ideals of Noetherian rings which are not irreducible

Is the radical of an irreducible ideal irreducible?

In $K[X,Y]$, is the power of any prime also primary?

A square matrix has the same minimal polynomial over its base field as it has over an extension field

Are there Zariski-continuous maps between algebraic sets that are not polynomial maps?

Linearly disjoint field extensions

Intersection of irreducible components of a smooth curve

When do two matrices have the same column space?

Noetherian integral domain such that $m/m^2$ is a one-dimensional vector space over $A/m$

What is the differences between scheme-theoretical intersection and set-theoretical intersection?

Proving $2,3,1+\sqrt{-5}$ and $1-\sqrt{-5}$ are irreducible in $\mathbb{Z}[\sqrt{-5}]$

Knot with genus $1$ and trivial Alexander polynomial?

Artinian local $k$-algebra

Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?

Invertible modules are locally free of rank 1

Prove that an infinite ring with finite quotient rings is an integral domain

Spectrum of finite $k$-algebras

Is there a $C^\infty$ function $f$ s. t. the convergent radius of Maclaurin series of $f$ is $0$?

Homology of $\mathbb{R}^3 - S^1$

Similar matrices and field extensions

How to Compute Genus

Stalk of coherent sheaf vanishing

Is invertibility a stalk-local property?

How to calculate the determinant of all-ones matrix minus the identity?